


from math import factorial







def SCREAMING_SNAKE_CASE	(			__lowerCAmelCase							,   __lowerCAmelCase				)    ->				int:

  # If either of the conditions are true, the function is being asked
  # to calculate a factorial of a negative number, which is not possible
  if n < k or k < 0:
    raise ValueError('''Please enter positive integers for n and k where n >= k'''				)
  return factorial(__lowerCAmelCase				) // (factorial(__lowerCAmelCase				) * factorial(n - k				))


if __name__ == "__main__":
   print(
       """The number of five-card hands possible from a standard""",
       F"""fifty-two card deck is: {combinations(5_2, 5)}\n""",
   )

   print(
       """If a class of 40 students must be arranged into groups of""",
       F"""4 for group projects, there are {combinations(4_0, 4)} ways""",
       """to arrange them.\n""",
   )

   print(
       """If 10 teams are competing in a Formula One race, there""",
       F"""are {combinations(1_0, 3)} ways that first, second and""",
       """third place can be awarded.""",
   )









'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  int = 1_000_000   ):
       """simple docstring"""




       a_						     =			set(range(3   ,       lowercase_   ,       2   )   )
       primes.add(2   )
       for p in range(3   ,       lowercase_   ,       2   ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p   ,       lowercase_   ,       lowercase_   )   )   )

       a_						     =			[float(lowercase_   ) for n in range(limit + 1   )]

       for p in primes:
              for n in range(lowercase_   ,       limit + 1   ,       lowercase_   ):
                     phi[n] *= 1 - 1 / p

       return int(sum(phi[2:]   )   )


if __name__ == "__main__":
  print(f"""{solution() = }""")




